Russia and China wrapped up joint military exercises on Wednesday in the Sea of Japan, the largest naval drills China has ever conducted with a foreign partner. The exercises took place amid mounting U.S. frustration over Russian and Chinese efforts to block United Nations Security Council action against the Assad regime in Syria and fuel U.S. concern about an anti-American axis between the two authoritarian great powers.

Although Chinese-Russian relations have improved in recent years as trade has expanded, old border disputes have been resolved, and the tempo of meetings between top leaders has increased, their collaboration masks serious differences. Only major missteps by the United States could make American fears a reality.

Moscow and Beijing characterize their relationship as a comprehensive strategic partnership, but their cooperation is mostly tactical. The two countries approach the world from quite different vantage points. China is a rising power, with a fast-growing, export-driven economy eager to benefit from globalization. Russia is a stagnating petro-state seeking to insulate itself from the forces of change.

Moscow touts its partnership with Beijing mostly to prove to the rest of the world that Russia still matters, while China views it as a low-cost way of placating Russia. Lacking much of a common agenda, cooperation is limited to areas where their interests already overlap, like bolstering trade.

In the parts of the world that matter most to them, Russia and China are more rivals than allies. Take Southeast Asia. Beijing’s assertive claims to maritime boundaries in the South China Sea have rattled America’s regional partners and led Washington to deepen its security cooperation with Vietnam, the Philippines and other states whose territorial claims China disputes. But to Beijing’s frustration, Moscow has remained silent on the territorial disputes, even as Russian energy companies have signed deals with Vietnam to develop oil and gas resources in the South China Sea — in waters claimed by China. Meanwhile, Russia’s defense industry is expanding its weapons sales throughout Southeast Asia, including selling advanced attack submarines to the Vietnamese Navy.

In Central Asia, Chinese economic power is rapidly pushing Russia aside. Chinese capital is paying for new roads, railroads and pipelines that lock the Central Asian states ever tighter into the Chinese embrace. Last year, all the Central Asian nations save Uzbekistan traded more with China than with Russia. Thanks to the opening of a gas pipeline from Central Asia to China in late 2009, Beijing has been able to take a hard line with Moscow on negotiations to build a new Russia-China pipeline. Russia’s push to bring Kyrgyzstan and Tajikistan into its customs union with Belarus and Kazakhstan, along with Vladimir Putin’s call to establish an Eurasian Union by 2015, are based heavily on a desire to limit the reorientation of the Central Asian states’ economies toward China.

Nor does sporadic cooperation between the Russian and Chinese militaries alter the fact that China’s assertiveness worries Russia at least as much as it worries the United States. Russian military commanders acknowledge that they see China as a potential foe, even as official statements continue to focus on the alleged threat from the United States and NATO. In July 2010, Russia conducted one of its largest ever military exercises, which aimed at defending the sparsely populated Russian Far East from an unnamed opponent with characteristics much like those of the People’s Liberation Army.

The only sense in which Russia and China are truly aligned is in their shared belief that the post-Cold War international order, designed by and for the United States, denies them their rightful place at the table, while allowing Washington to throw its weight around without regard for the interests of others.

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This sense of exclusion underpins their support for new institutional mechanisms like the Shanghai Cooperation Organization, the so-called BRICS countries and the Group of 20, as well as their portrayal of the U.N. Security Council as the sole legitimate arbiter of war and peace.

Much Chinese-Russian cooperation, especially at the U.N., is based on defending the right of states to be fully sovereign within their own borders and opposing intervention in internal affairs without Security Council approval. Even this stand is less about high principle than about protecting concrete interests. Moscow ignored Georgia’s sovereignty to recognize the independence of South Ossetia and Abkhazia in 2008 — to which China objected less from principle than because of the potential precedent for Taiwan.

Beijing and Moscow also abstained when the Security Council authorized a no-flight zone in Libya, a country of little strategic significance for either of them. Their harder line on Syria is a reflection of Russia’s political stakes in that country, with China happy to hide behind Russian objections to prevent another instance of U.S. intervention.

The lesson for the United States is that the more it dismisses Russian and Chinese demands that their concerns be taken into account, the more its fears about a Chinese-Russian axis become self-fulfilling. Where Moscow or Beijing have real interests at stake — as Russia does in Syria — Washington should be prepared to listen, and to engage in a real give-and-take before acting.

Washington also should take seriously the argument that institutions designed for the post-Cold War world do not reflect the real distribution of power today. It should also be open to new formats, such as the G-20, that place Russia and China on equal footing with traditional U.S. partners. This is especially relevant in Asia, where a new security architecture is still being designed.

Giving Beijing and Moscow more of a stake in the running of the world might be uncomfortable, but the alternative is bringing the Chinese-Russian axis that U.S. policy makers fear closer to reality.